ON THE COLOURS OF THICK PLATES. 187 But to prevent any doubt as to whether the bands might not have been too small to be seen when formed by transmission, I have calculated the retardation in the same manner as in Art. 10. The result is where R is the retardation of the stream scattered at emergence relatively to that scattered at entrance, c is the distance of the luminous point from the plate, h that of the plate from the eye, t the thickness, and //- the refractive index of the plate, and as, y are the co-ordinates of the point in which the plate is cut by any small pencil (regarded as a ray) which enters the eye, and are measured from the point in which the plate is cut by a line joining the luminous point and the eye, a line to which the plane of the plate is supposed to be perpendicular. On substituting numerical values in the above formulae, it appeared that the dimensions of the rings were such that they could not possibly have escaped notice had they really been formed. The non-appearance of the rings leads to the following law. In order that two streams of scattered light may be capable of interfering, it is necessary tliat they should be scattered, in passing and repassing, by the same set of particles. Two streams which have been scattered by two different sets of particles, although they may have come originally from the same source, behave with respect to each other like two streams coming from different sources. According to this law, in all calculations relating to the colours of thick plates, we must consider the elementary system of rings or bands corresponding to each element of the dimmed surface of the mirror, and then conceive these elementary systems superposed. We must not compound the vibrations corresponding to streams which have been scattered by different elements, and then find the resulting illumination. 28. The reason of this law will be apparent if it be considered that particles of dust, &c. small as they may bo, arc usually large in comparison with waves of light, so that tho light scattered at entrance, taken as a whole, is most irregular; and the only reason why regular interference is possible at all is, that each particle of dust acts twice in a similar manner, once when the general wave is going, and again when it is returning.